Question

Rakesh calculated the average of 7 numbers as 27. The average of the first two numbers is 9 and that of the next two numbers is 14. If the fifth number is twice the sixth one and the sixth number is 50% more than the seventh number, then find the seventh number. 
1. 78
2. 26
3. 39
4. 65

Answer 1

Correct Answer - Option 2 : 26

Given:

Average of 7 numbers = 27

Average of first two numbers = 9

Average of next two numbers = 14

Formula Used:

Average = Sum of terms/Number of terms

Calculations:

Let fifth, sixth and seventh numbers be x, y, z respectively.

As x is twice of y and y is 50% more than z.

⇒ x : y = 6 : 3, y : z = 3 : 2

⇒ x : y : z = 6 : 3 : 2

Total sum of 7 terms = 7 × 27 = 189

Sum of first 2 terms = 9 × 2 = 18

Sum of next 2 terms = 14 × 2 = 28

Total sum = Sum of first 2 terms + Sum of next 2 terms + x + y + z

⇒ 189 = 18 + 28 + x + y + z

⇒ x + y + z = 143

1 unit = 130/(x + y + z) = 143/11

⇒ 1 unit = 13

⇒ x = 6 × 13 = 78

     y = 3 × 13 = 39

     z = 2 × 13 = 26

∴ The value of seventh number is 26.